L. GOCH – FEBRUARY 2011L. GOCH – FEBRUARY 2011

Basic Statistics Using Basic Statistics Using MinitabMinitab

AGENDA

Comparing 1 Group to a Target / Specification OR Comparing 2+ Groups to Each Other:

1) Stability – Run Chart (Feb 4th) or Control Chart (Mar 4th)2) Shape – Histogram (Feb 4th) or Probability Plot3) Spread – Test for Equal Variances 4) Centering – 1-Sample T-test, 1-Sample Sign, Paired

T, 2-Sample T-test, ANOVA or Mood’s Median Test Comparing Proportions - 1 Proportion, 2

Proportion

Basic Linear Regression – Fitted Line Plot

Chi-Squared – Cross Tabulation and Chi-Square

Trend Analysis – Under Stat > Time Series: We won’t be covering in this class. See Tutorials for more information.

Basic Statistics using Minitab.mtb

PROBABILITY PLOT: PROBABILITY PLOT:

GRAPH > PROBABILITY PLOT

PROBABILITY PLOT: GRAPH > PROBABILITY PLOT

Use to display overlaid probability plots of multiple variables and/or multiple groups on the same graph.

Open worksheet FlameRTD.mtwFlameRTD.mtw

PROBABILITY PLOT

5.04.54.03.53.02.52.0

99

95

90

80

70

6050

40

30

20

10

5

1

Fabric1

Per

cent

90

3.54

4

3.18

5

4.30

4

3.013 0.4138 15 0.321 0.4972.727 0.3575 15 0.545 0.1333.573 0.5700 15 0.310 0.517

Mean StDev N AD P

ABNone

Coating

Probability Plot of Fabric1Normal

is NORMALLY DISTRIBUTED.0.05, conclude each data setSince all p-values are >

TEST FOR EQUAL TEST FOR EQUAL VARIANCES: VARIANCES:

STAT > ANOVA > TEST FOR EQUAL VARIANCES

TEST FOR EQUAL VARIANCES: STAT > ANOVA > TEST FOR EQUAL VARIANCES

Use to display overlaid probability plots of multiple variables and/or multiple groups on the same graph.

Open worksheet FlameRTD.mtwFlameRTD.mtw

TEST FOR EQUAL VARIANCES (SESSION WINDOW & GRAPH RESULTS)

None

B

A

1.11.00.90.80.70.60.50.40.30.2

Coat

ing

95% Bonferroni Confidence Intervals for StDevs

Test Statistic 3.19P-Value 0.203

Test Statistic 1.42P-Value 0.253

Bartlett's Test

Levene's Test

Test for Equal Variances for Fabric1

Use for Normal Data

Use for Non-Normal Data

CENTERING COMPARISON CENTERING COMPARISON ANALYSESANALYSES

Analysis # of Grps Comparison Statistic1-Sample T 1 Target Average1-Sample Sign 1 Target Median

Paired T 2Paired Data (e.g. before

vs after)Difference

2-Sample T 2 Each Other AverageANOVA 2+ Each Other AverageMood’s Median Test 2+ Each Other Median

Response is Numeric & Factors are Text or Numeric

1-SAMPLE T-TEST: 1-SAMPLE T-TEST:

STAT > BASIC STATISTICS > 1-SAMPLE T

1-SAMPLE T-TEST: STAT > BASIC STATISTICS > 1-SAMPLE T

Performs a one-sample t-test or t-confidence interval for the mean.

Open worksheet EXH_Stat.mtwEXH_Stat.mtw

1-SAMPLE T (SESSION WINDOW & GRAPH RESULTS)Note: For n<30, data is assumed to be Normally Dist’d

5.15.04.94.84.74.64.54.4

X_

Ho

Values

Boxplot of Values(with Ho and 95% t-confidence interval for the mean)

95% of the time the True Avg will be between 4.5989 & 4.9789

The sample Avg is significantly different from the Target of 5.

1-SAMPLE SIGN: 1-SAMPLE SIGN:

STAT > NONPARAMETRICS> 1-SAMPLE SIGN

1-SAMPLE SIGN: STAT > NONPARAMETRICS> 1-SAMPLE SIGN

Performs a one-sample t-Sign or t-confidence interval for the median.

Open worksheet EXH_Stat.mtwEXH_Stat.mtw

1-SAMPLE SIGN (SESSION WINDOW RESULTS)

95% of the time the True Median will be between 108.5 & 211.7

The sample Median is NOT significantly different from the Target of 115.

PAIRED T-TEST: PAIRED T-TEST:

STAT > BASIC STATISTICS > PAIRED T

PAIRED T-TEST: STAT > BASIC STATISTICS > PAIRED T

Tests the mean difference between paired (related) observations.

Open worksheet EXH_Stat.mtwEXH_Stat.mtw

PAIRED T (SESSION WINDOW & GRAPH RESULTS)

95% of the time the True Avg Difference will be between -0.687& -0.133 which does NOT contain ZERO.

The sample Avgs are significantly different from each other.

0.0-0.3-0.6-0.9-1.2

X_

Ho

Differences

Boxplot of Differences(with Ho and 95% t-confidence interval for the mean)

2-SAMPLE T-TEST: 2-SAMPLE T-TEST:

STAT > BASIC STATISTICS > 2-SAMPLE T

2-SAMPLE T-TEST: STAT > BASIC STATISTICS > 2-SAMPLE T

Performs a two-sample t-test or t-confidence interval for the mean difference.

Open worksheet Furnace.mtwFurnace.mtw

2-SAMPLE T (SESSION WINDOW & GRAPH RESULTS)

95% of the time the True Avg Difference will be between -1.450 & 0.980 which contains ZERO.

The sample Avgs are NOT significantly different from each other.

21

20

15

10

5

Damper

BTU

.In

Boxplot of BTU.In

ONE-WAY ANOVA: ONE-WAY ANOVA:

STAT > ANOVA > ONE-WAY

ONE-WAY ANOVA: STAT > ANOVA > ONE-WAY

Compares the Averages for 2 or more Groups.

Open worksheet Exh_AOV.mtwExh_AOV.mtw

ONE-WAY ANOVA (SESSION WINDOW & GRAPH RESULTS)

At least 1 Pair of Avgs are significantly different from each other.

4321

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

Carpet

Dura

bility

Boxplot of Durability

MOOD’S MEDIAN TEST: MOOD’S MEDIAN TEST:

STAT > NONPARAMETRICS> MOOD’S MEDIAN TEST

MOOD’S MEDIAN TEST: STAT > NONPARAMETRICS> MOOD’S MEDIAN TEST

Compares the Medians of 2 or more Groups.

Open worksheet Cartoon.mtwCartoon.mtw

MOOD’S MEDIAN TEST (SESSION WINDOW RESULTS)

Group 2 is significantly different from groups 0 & 1 since the 95% CI’s do NOT overlap.

At least one group’s median is significantly different from the others.

210

140

130

120

110

100

90

80

70

ED

Otis

Boxplot of Otis

1-PROPORTION TEST: 1-PROPORTION TEST:

STAT > BASIC STATISTICS > 1-PROPORTION

1-PROPORTION: STAT > BASIC STATISTICS > 1-PROPORTION

Performs a one-sample proportions test or p-confidence interval for a proportion.

No worksheet is needed for this test.

1-PROPORTION: (SESSION WINDOW RESULTS)

Note: Proportion Testing Should NOT be done when the sample size n<30!!

95% of the time the True Proportion will be between 55.74% & 62.10%

The sample Proportion is significantly different from the Target of 65%.

2-PROPORTION TEST: 2-PROPORTION TEST:

STAT > BASIC STATISTICS > 2-PROPORTIONS

2-PROPORTIONS: STAT > BASIC STATISTICS > 2-PROPORTIONS

Performs a two-sample proportions test or p-confidence intervals for a proportion.

No worksheet is needed for this test.

2-PROPORTIONS: (SESSION WINDOW RESULTS)

Note: Proportion Testing Should NOT be done when the sample size for any one group is <30!!

95% of the time the True Difference between the Proportions will be between -9.58% & 17.58%

The difference in Proportions is NOT significantly different.

BASIC LINEAR BASIC LINEAR REGRESSION: REGRESSION:

STAT > REGRESSION > FITTED LINE PLOT

REGRESSION: STAT > REGRESSION > FITTED LINE PLOT

Performs a Regression Analysis on 1 Input (X) and 1 Output (Y).

Open worksheet Exh_REGR.mtwExh_REGR.mtw

REGRESSION: (GRAPH RESULTS)

3025201510

40

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0

MachineSetting

Energ

yConsu

mption

S 12.1825R-Sq 2.3%R-Sq(adj) 0.0%

Fitted Line PlotEnergyConsumption = 1.25 + 0.3218 MachineSetting

The line does NOT fit the curved data. Need a quadratic, cubic or transformation of the data.

REGRESSION: (SESSION WINDOW & GRAPH RESULTS)

The Regression Equation shows that Machine Setting explains 93.1% of the variability in Energy Consumption.

The Quadratic Term is significant in the model. NOTE: If a higher order term is significant than the lower order term must remain in the model.

3025201510

100

10

1

MachineSetting

Energ

yConsu

mption

S 0.167696R-Sq 93.1%R-Sq(adj) 91.1%

Fitted Line Plotlog10(EnergyConsumption) = 7.070 - 0.6986 MachineSetting

+ 0.01740 MachineSetting**2

CROSS TABULATION CROSS TABULATION AND CHI-SQUARE: AND CHI-SQUARE:

STAT > TABLES > CROSS TABULATION AND CHI-SQUARE

CHI-SQUARE: STAT > TABLES > CROSS TABULATION AND CHI-SQUARE

Performs a Chi-Squared Analysis on Count Data.Open worksheet Exh_TABL.mtwExh_TABL.mtw

CHI-SQUARE ANALYSIS: (SESSION WINDOW RESULTS)

No significant association between Gender and Activity

CONCLUSIONS

Results need to be Supported by data Not based on conjecture or intuition Shown in 1) Graphical & 2) Statistical 1) Graphical & 2) Statistical

formatformat Make sense from an 3) Engineering 3) Engineering

standpointstandpoint Use P-values to determine if Results could have

happened by Chance!!Need Significant Differences Need Significant Differences for Reliable Conclusions !!for Reliable Conclusions !!Need Significant Differences Need Significant Differences for Reliable Conclusions !!for Reliable Conclusions !!